We follow the expansion in modes for the Dirac fields proposed in [1]}, [2]}. We write the following Fourier expansion of the Dirac field operator
\(\psi (x)=\frac{1}{\sqrt{(2\pi )^3a^{3}}} \int d^3\vec{k} \sum _{\lambda }\left[B_{\vec{k} \lambda } e^{i\vec{k} \vec{x}} u_{\vec{k} \lambda }(x)+D_{\vec{k} \lambda }^{\dagger } e^{-i\vec{k} \vec{x}}v_{\vec{k} \lambda }(x) \right] \ , \) 
